1. Field
One feature relates to digital filters, and more particularly, to methods and devices for reducing steady state error in fixed point recursive filters.
2. Background
In signal processing, a recursive filter is a type of filter that re-uses one or more of its outputs as an input. This feedback typically results in an unending impulse response (commonly referred to as infinite impulse response (IIR)), characterized by either exponentially growing, decaying, or sinusoidal signal output components. Therefore, recursive filters may also be known as infinite impulse response filters (IIR filters). FIGS. 1 and 2 illustrate single-tap 100 and two-tap 200 recursive filters, respectively, found in the prior art.
Floating point recursive filters may eventually converge to an output value having no steady state error. That is, the final output value of the floating point recursive filter equals the expected value without non-linear deviation. However, floating point implementations are computationally expensive and may be impractical in many applications. Thus, fixed point implementations of recursive filters are often needed in many applications due to time and power constraints. However, due to the limited bit-width, fixed point recursive filters exhibit non-linear behavior at certain operating points. In addition to the expected quantization and saturation effects, fixed point implementations suffer from non-zero steady state error. This is a limitation that can significantly impact devices, such as a mobile phone, that may use the recursive filter to estimate the signal to noise ratio of a downlink channel.
Therefore, there is a need to eliminate or at least reduce the non-zero steady state errors of fixed point recursive filters.